Airport parking space distribution method, system, equipment and medium

Abstract

The invention discloses an airport parking space distribution method, system and device and a medium, and relates to the technical field of parking space distribution, and the method comprises the steps: obtaining a plurality of parking spaces and flights of different airport models; the corresponding relation between the parking spaces and the flights is used as a decision variable, and the most balanced parking space idle time, the minimum passenger walking distance and the least far parking space distribution number are used as objective functions. Taking the maximum utilization rate of the large-scale gate position, the maximum overall utilization rate of the gate position, and the maximum gate position and flight matching rate as constraint conditions to construct a gate position distribution optimization model; an improved sparrow search algorithm is adopted to solve the gate position distribution optimization model, and a global optimal solution and the fitness of the global optimal solution are generated; and allocating the airport parking spaces according to the global optimal solution and the fitness thereof.

Description

Technical Field

[0001] The present invention relates to the technical field of parking stand allocation, and in particular to an airport parking stand allocation method, system, equipment and medium. Background Art

[0002] With the continued, rapid, and vigorous development of the global air transport industry, civil airports, as aviation transport infrastructure, air traffic take-off and landing venues, and the basis for airport-related economic development, are becoming increasingly important in global urban connectivity, the construction of integrated transportation systems, and the development of the national economy. The rapid annual growth in air transport volume has led to a serious problem of insufficient airport capacity. Considering cost and time constraints, expanding airport ground facilities such as runways, boarding gates, and taxiways is not a feasible solution to increase airport capacity. How to rationally dispatch limited airport surface resources and improve utilization has become a key anchor for the development of the aviation industry. As an important part of airport operations management, optimized parking stand scheduling is a key factor in achieving rapid and safe flight docking, ensuring effective connections between flights, and improving the capacity and service efficiency of the entire airport system.

[0003] The parking stand allocation optimization problem aims to assign appropriate parking stands to each operating flight while satisfying certain constraints and objectives. This problem is inherently complex due to its multi-constraint and multi-resource nature, and is subject to numerous factors, including airline-specific factors, traffic flow control, and weather conditions, making it a standard NP-hard problem. The Sparrow Search Algorithm (SSA) is a new swarm intelligence optimization algorithm proposed by Xue Jiankai. The SSA sets rules based on the foraging and regurgitation behaviors of sparrows, and simulates the search for a global optimal solution. Due to its simple implementation, strong optimization capabilities, and rapid convergence, the algorithm has been improved upon by many researchers and applied to research in various fields. Key improvements to SSA include population initialization, strategy adjustment for the finder-follower pair, dynamic parameter setting, and integration with other intelligent optimization algorithms. Some scholars have proposed an improved sparrow search algorithm (OBL-SA-SSA), which introduces an adversarial learning (OBL) strategy to optimize the initial population, improving population quality and local search capabilities. Combining the Metropolis criterion of the simulated annealing algorithm (SA), it accepts new solutions with a certain probability, enhancing the algorithm's global search capabilities and ability to escape local optima, effectively improving the efficiency and path quality of mobile robot path planning. Some scholars have proposed a new chaotic sparrow search algorithm (NCSSA), which uses a greedy method and cubic chaotic mapping to initialize the population, improving the uniformity and diversity of the population. A new reconnaissance and warning position update formula has been designed to enhance the algorithm's global search capabilities. The introduction of Gaussian mutation, insertion mutation, and reverse order local search strategies enables the algorithm to effectively escape local optima, ultimately achieving higher accuracy and efficiency in solving the TSP problem. Some scholars have introduced a periodic adaptive convergence factor, adopted a dynamic adjustment strategy for the number of discoverers, and introduced an adaptive spiral search strategy, which improved the convergence speed of the algorithm and enhanced the global exploration capability of the algorithm. Ultimately, shorter paths and better search performance were achieved in UAV path planning. Parallelism, strong adaptability, and strong global search capabilities make swarm intelligence algorithms particularly effective in solving complex and large-scale optimization problems.

[0004] However, existing approaches to the parking stand allocation problem suffer from the following drawbacks: While exact algorithms based on integer programming or mixed-integer linear programming can guarantee theoretically optimal solutions, their computational complexity grows exponentially with the problem size, making them difficult to meet the real-time scheduling requirements of large airports. Heuristic algorithms (such as genetic algorithms and greedy strategies) improve computational efficiency but are prone to local optimal solutions and lack multi-objective coordination, resulting in high parking stand availability, redundant taxiing distances, and excessive passenger walking distances. Static optimization models are insufficiently adaptable to dynamic flight disturbances, which can easily lead to cascading delays. Data-driven approaches are limited by data noise and sparsity, significantly reducing their generalization performance. Furthermore, existing methods often employ fragmented optimization, neglecting the coordinated scheduling of parking stands, gates, and ground handling equipment, exacerbating resource conflicts and operating costs. These drawbacks collectively hinder overall airport operational efficiency and service quality, necessitating the urgent need for novel optimization strategies that combine dynamic response, multi-objective balance, and cross-system coordination. Summary of the Invention

[0005] In view of the shortcomings of existing technologies, such as being prone to falling into local optimal solutions and lacking multi-objective coordination capabilities, which lead to high parking stand vacancy rates, redundant taxiing distances, and long passenger walking distances, making it difficult to meet the real-time scheduling needs of large airports, the present invention proposes an airport parking stand allocation method, system, equipment, and medium. By designing a hybrid multi-strategy and multi-mechanism sparrow search algorithm with good optimization performance and robustness, the method solves the airport boarding gate allocation, thereby greatly improving the problems existing in the existing technology.

[0006] A method for allocating parking spaces at an airport comprises the following steps: Obtain multiple parking stands and flights of different airport models; use the correspondence between parking stands and flights as the decision variable, and the objective function of maximizing the idle time of parking stands, minimizing the passenger walking distance, and minimizing the number of remote parking stands. Construct a parking stand allocation optimization model with the maximum utilization rate of the largest parking stand, the maximum overall parking stand utilization rate, and the maximum parking stand and flight matching rate as constraints. The allocation schemes of all flights and parking spaces are regarded as a population, and each flight and parking space allocation scheme is regarded as an individual. The minimization of the objective function is used as the fitness function, and the improved sparrow search algorithm is used to solve the parking space allocation optimization model. The solution process specifically includes: generating an initial population, calculating the adaptive variation quasi-reflective solution for each individual in the initial population, calculating the fitness value of each individual and the adaptive variation quasi-reflective solution, selecting the individual with the better current fitness value to update the initial population, and obtaining the updated population; calculating the fitness value of each individual in the updated population and sorting them, and determining the discoverer individual, follower individual, and guard individual; generating a random number for each discoverer individual, and if the random number is less than the set threshold, triggering the Levy flight strategy and generating the Levy step size; updating the discoverer individual position according to the Levy step size; the follower individual moves closer to the discoverer individual according to the random perturbation, and at the same time introducing the vertical and horizontal cross strategy to update the position of each guard individual, and generating the optimal allocation plan between flights and parking spaces; Allocate airport parking spaces based on the optimal allocation plan between flights and parking spaces.

[0007] Furthermore, the objective function of achieving the most balanced parking stand idle time, minimizing passenger walking distance, and minimizing the number of remote stands is specifically as follows: calculating the idle time of each parking stand between consecutive uses, summing the idle time of all parking stands, and obtaining the optimization objective of achieving the most balanced parking stand idle time, which is expressed as: According to the shortest walking distance between passengers and parking stands, the optimization goal of minimizing the walking distance of passengers is obtained, which is expressed as: According to the distance between the parking stand and the terminal, the optimization goal is to minimize the number of flights at the gate farthest from the parking stand, which can be expressed as: ; in, Indicates parking space On the flight Free time before arrival; Indicates parking space Free time after daily closing tasks are completed; Indicates the number of parking spaces. n Indicates the total number of flights, Represents the corresponding optimization objective function; Indicates the actual allocated parking space flights the number of passengers; Indicates that the passenger has arrived at the boarding gate Required walking distance, is the decision variable for allocating flights to parking spaces. If flight Assigned to a parking stand ,but , otherwise 0; is the remote stand usage indicator variable. If the flight Assigned to a remote stand ,but , otherwise it is 0. The remote parking stand is the parking stand whose distance to the flight is greater than the set distance threshold.

[0008] Furthermore, the constraints of the maximum utilization rate of large parking stands, the overall utilization rate of the maximum parking stands, and the maximum parking stand and flight matching rate specifically include: A flight can only occupy one parking space within the specified time, which is expressed as: The parking stand size and flight size are divided into three categories according to actual conditions. The size of the flight parked on the parking stand must not exceed the parking stand size, which is expressed as: The pushback time between two consecutive flights at the same parking stand must be at least the set safety time, which is expressed as: The parking spaces are divided into three types: large, medium, and small according to the threshold value. The optimization goal is to maximize the utilization rate of large spaces, which can be expressed as: Maximize the overall utilization of the boarding gate and speed up the flight turnaround, expressed as: Minimize the matching difference between flights and slots, expressed as: ; in, Represents a 0-1 variable indicating the flight Assigned to the apron; Indicates the model of the parking stand; Indicates the flight type; Indicates flight k Arrival time; Indicates flight k departure time; Indicates flight i Parking at a gate that is not the correct size for the aircraft j Department; Indicates flight i Assigned to a large parking stand j .

[0009] Furthermore, the step of calculating the reverse solution and the quasi-reverse solution for each individual in the population and calculating the adaptive mutation rate according to the current number of iterations specifically includes the following steps: Constraining the quasi-reverse solution to the area near the midpoint of the line connecting the current solution and the reverse solution yields: ; ; in, 、 Indicates the middle value of the range. represents the solution of the current generation of quasi-reflective learning, is a random factor between 0 and 1, represents the solution of this generation of mutational quasi-reflective learning; By introducing adaptive mutation rate to dynamically integrate the global exploration of OBL and the local development of QOBL, we can obtain: ; ; in α is the attenuation parameter, and represent the minimum mutation rate and the maximum mutation rate, respectively. Indicates the location of the current iteration initialization solution; represents the random variation parameter; T represents the total number of iterations, represents the solution of reverse learning.

[0010] Furthermore, a random number is generated for each individual discoverer. If the random number is less than a set threshold, Levy flight is triggered, a Levy step length is generated, and the individual discoverer position is updated according to the Levy step length. The process is expressed as follows: ; ; in Indicates the i Only the sparrow is iterating t +1 position, is the step size factor used to control the magnitude of the Levy step size, Represents the random step size generated by Levy distribution, satisfying , s represents the step size reference value, where , Is a uniformly distributed random number used to trigger the Levyflight strategy is the trigger threshold, is a stabilizing parameter used to control the shape of the step size distribution; 𝜆 controls the jump amplitude of the Levy distribution; 𝑄⋅𝐿 represents the random disturbance term composed of the disturbance factor 𝑄 and the step size 𝐿.

[0011] Furthermore, the vertical and horizontal cross strategy is introduced to update the position of each individual sentry, specifically including the following steps: For the Vigilant , select paired individuals according to their position parity, when j When it is an odd number, the next individual j +1 crossover, when j When it is an even number, it is the same as the previous individual j -1 crossover, which are represented by: in Indicates the j Individuals in i Dimensional location; r represents a uniformly distributed random number, ; c is the disturbance factor, ; At the same time, for each individual vigilant , randomly select two of its dimensions and , to fuse information between dimensions: in is a uniformly distributed random number, ; represents two different dimensions randomly selected from the dimension set, 、 、 Respectively represent the updated j The first vigilante i Dimensional location information.

[0012] The present invention also includes an airport parking stand allocation system, comprising: The model building module is used to obtain multiple parking stands and flights of different airport models. Using the correspondence between parking stands and flights as the decision variable, and the most balanced parking stand idle time, minimized passenger walking distance, and the minimum number of remote stands assigned as the objective function, a parking stand allocation optimization model is constructed with the maximum utilization rate of the largest parking stand, the maximum overall parking stand utilization rate, and the maximum parking stand and flight matching rate as constraints. The solution module is used to treat the allocation plans of all flights and parking spaces as a population, and the allocation plan of each flight and parking space as an individual, with the minimization of the objective function as the fitness function, and adopt the improved sparrow search algorithm to solve the parking space allocation optimization model; the solution process specifically includes: generating an initial population, calculating the adaptive variation quasi-reflective solution of each individual in the initial population, and selecting the individual with the better current fitness value to update the initial population by calculating the fitness value of each individual and the adaptive variation quasi-reflective solution to obtain an updated population; calculating the fitness value of each individual in the updated population and sorting them to determine the discoverer individual, follower individual and guard individual; generating a random number for each discoverer individual, and if the random number is less than the set threshold, triggering the Levy flight strategy and generating the Levy step length; updating the discoverer individual position according to the Levy step length; the follower individual moves closer to the discoverer individual according to the random perturbation, and at the same time introducing the vertical and horizontal cross strategy to update the position of each guard individual to generate the optimal allocation plan between flights and parking spaces; The allocation module is used to allocate airport parking spaces according to the optimal allocation plan between flights and parking spaces.

[0013] The present invention also includes an airport parking stand allocation computer device, comprising: a memory, a processor, and a computer program stored in the memory, wherein the processor implements the steps of the airport parking stand allocation method when executing the computer program.

[0014] The present invention also includes a readable storage medium, wherein the readable storage medium stores a computer program, wherein the computer program includes program instructions, and when the program instructions are executed by a processor, they are used to execute the steps of the airport parking space allocation method.

[0015] The present invention provides an airport parking space allocation method, which has the following beneficial effects: The present invention aims at the parking stand allocation optimization model with the goals of most balanced parking stand idle time, minimized passenger walking distance, least number of remote parking stands allocated, maximum utilization rate of large parking stands, maximum overall utilization rate of parking stands, and maximum parking stand and flight matching rate. A hybrid multi-strategy and multi-mechanism sparrow search algorithm MRCFSSA with good optimization performance and robustness is proposed; an adaptive variation reflection learning strategy is designed to initialize the population, which fully expands the global search space and increases the diversity of the population, thereby improving the quality of the initial solution; based on the vertical and horizontal crossover algorithm, a vertical and horizontal crossover mechanism is designed in combination with the sentinel stage of the sparrow search, which enhances the global search ability of the algorithm and avoids falling into the local optimum with the increase of the number of iterations; the follower stage adopts the Levy flight strategy, which realizes the dynamic balance between extensive exploration of the global solution space in the early stage and jumping out of the local optimum in the later stage in the algorithm through its unique heavy-tailed distribution random step size characteristics, thereby effectively coordinating the relationship between global search and local development; the present invention proposes MRCFSSA based on adaptive variation quasi-reflective learning, vertical and horizontal crossover strategy and Levy The combination of the three flight strategies creates a multi-objective model for the parking stand allocation problem, which comprehensively considers six key indicators: parking stand availability balance, passenger walking distance, and minimization of remote stand allocation. This model generates the optimal allocation plan between flights and parking stands. Compared with traditional algorithms, it significantly improves resource utilization efficiency and enhances the passenger experience (by shortening walking distance), and provides an efficient solution for complex dynamic airport scheduling. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 Schematic diagram of an adaptive quasi-reflective learning strategy in an embodiment of the present invention; Figure 2 This is a schematic diagram of the number of flights corresponding to parking stands in an embodiment of the present invention; Figure 3 This is a schematic diagram of a Gantt chart of parking stands and flights in an embodiment of the present invention; Figure 4 Schematic diagram of iterative curves for solving the parking space allocation problem using different algorithms in an embodiment of the present invention; Figure 5 The figure is a flow chart of a method for allocating airport parking spaces according to an embodiment of the present invention. DETAILED DESCRIPTION

[0017] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0018] The proposed sparrow search algorithm is an optimization algorithm based on swarm intelligence, inspired by the foraging behavior of sparrows in nature. During foraging, sparrows constantly adjust their positions to maximize their food supply. Based on the quality of their foraging, sparrows can be divided into two groups: finders and joiners. Finders search large areas, providing foraging areas and directions. Joiners follow the information provided by finders and conduct localized searches. Meanwhile, the sparrows remain vigilant against predators, helping them find the optimal foraging area. The basic mechanism of sparrow search is described below:

[0019] The rule of the discoverer: Individuals with higher fitness in the sparrow population will act as discoverers to conduct a large-scale search of the foraging area, thereby screening the foraging area for the entire population and providing foraging directions. During each update iteration, the position change of the discoverer is related to the random parameter and the current iteration number. The formula is:

[0020] in, t Indicates the current iteration number, Represents the maximum number of iterations. Storage i A sparrow in the j Dimensional location information. α is a random parameter α ∈(0,1]. Q is a random number that follows a normal distribution, L is a size of 1* n ( n is a matrix of all ones of dimension . and ST Represent the warning value and safety threshold respectively, where ∈[0,1], ST ∈[0.5,1]. When < ST This means that the foraging environment is safe and the discoverer can continue to perform extensive search operations in the current environment. ≥ ST , means that the sparrow perceives that the environment may be dangerous, so it adopts a random movement strategy to avoid potential risks. In this way, the algorithm is able to balance between exploration and exploitation, thereby improving search efficiency and global optimization capabilities.

[0021] Joiner's rules: During foraging, the joiner constantly monitors the discoverer's position. If the joiner finds itself far away from the discoverer, it may be trapped in a local optimum, so it attempts to move closer to the global worst position to escape the current bad area. If the joiner finds itself close to the discoverer, it will conduct a local search around the discoverer to try to find a better solution. The joiner's position update is described as follows:

[0022] ; in, The discoverer was t +1 is the optimal position occupied by the generation, It indicates the current worst global position. A Represents a 1×n (n is the dimension) matrix, where each element is randomly assigned a value of 1 or -1. The calculation formula is as follows:

[0023] ; The watchdog's rule: During the iteration process, the number of sparrows aware of danger accounts for 10%-20% of the sparrow population. The main task of the watchdog is to monitor other sparrows in the population and adjust their position according to changes in the environment to avoid being attacked by predators.

[0024] ; in, Represents the current global optimal position. β As the step size control parameter, it is a random number that obeys a normal distribution with a mean of 0 and a variance of 1. K ∈[-1,1] is a random number that controls the step size of the sentry's movement. It is the fitness value of the current sparrow individual. and are the current global best and worst fitness values ​​respectively. ε is the smallest constant that avoids zero in the denominator.

[0025] > Indicates that the current position of the sentinel is at the edge of the population, and its fitness value is better than the global optimal solution. Because it is at the edge, the sentinel is more vulnerable to attacks by predators. For safety, the sentinel will move closer to the best position in the population. When = When , it means that the sentry is currently in the middle of the population. In order to reduce the risk of being preyed upon, the sentry will try to get closer to other sparrows and increase safety by adjusting its position.

[0026] The present invention proposes a multi-objective dynamic optimization allocation method for airport parking stands based on multi-strategy sparrow search, and proposes a hybrid multi-strategy multi-mechanism sparrow search algorithm (MRCFSSA) with good optimization performance and robustness, and applies it to solving the airport parking stand allocation problem; designs a population initialization method of adaptive mutation quasi-reflective learning to improve the quality of the initial solution, thereby increasing the convergence speed of the algorithm. Based on the vertical and horizontal cross algorithm, a vertical and horizontal cross mechanism is proposed to improve the performance of the algorithm and enhance the global search capability of the algorithm. The Levy flight strategy is used to balance the relationship between global search and local development, and the search space is dynamically adjusted to avoid a decrease in search capability; such as Figure 5 As shown, the specific steps include:

[0027] S1. Improving airport operational efficiency is closely linked to the rational configuration of boarding gates. Scientifically allocating boarding gates can not only improve airport operational efficiency and optimize passenger travel experience, but is also an important reference for airport planning, helping to promote the rational use of resources and ensure efficient and stable operation of the airport. However, boarding gate allocation is a complex combinatorial optimization problem involving multiple constraints. Traditional methods often find it difficult to balance efficiency and accuracy when solving it. Since the hybrid multi-strategy multi-mechanism sparrow search algorithm MRCFSSA has good global optimization capabilities, a fast convergence speed and high convergence accuracy, and the ability to handle complex problems, it is applied to solve the airport boarding gate allocation problem, and an airport boarding gate allocation method based on MRCFSSA is proposed. Experimental results show that this method can effectively solve the airport boarding gate allocation problem in actual projects, providing a new idea and method for airport planning, with high application value and promotion significance.

[0028] Multi-objective modeling of parking stand allocation: As the core link of airport ground scheduling, parking stand allocation involves multi-dimensional resource coordination and complex operating rules. Based on the optimization theory of operations research, this engineering problem can be transformed into a combinatorial optimization model with multiple constraints. Specifically, it is necessary to accurately describe the actual operating rules of the airport through mathematical language and establish a three-tuple model framework containing decision variables, objective functions and constraints. Among them, the decision variables represent the correspondence between flights and parking stands, the constraint system reflects physical limitations and operating specifications, and the objective function quantitatively evaluates the pros and cons of the allocation plan. Before establishing the model, it is necessary to define and specify the parameters and variables used in the model, as shown in Table 1.

[0029] Table 1 Definition of parameters and variables S1.1. Constraints include: (1) Uniqueness restriction: A flight can only occupy one parking space within a specified time. The formula is as follows: in, A binary decision variable is defined. If a flight is assigned to a parking slot, then =1, otherwise x =0, Represents a 0-1 variable indicating the flight i Assigned to the apron.

[0030] (2) Matching flight and parking stand sizes: The parking stand size and flight size are divided into three categories according to the actual situation. The size of the flight parked on the parking stand must not exceed the size of the parking stand to ensure the normal push-in and push-out of flights. The formula is as follows: in, Indicates the model of the parking space. Indicates the flight model.

[0031] (3) Safety time interval: To ensure flight safety and reduce the risk of delays, the push-out time of two flights at the same parking position should be at least a certain safety time apart. This can not only ensure safety but also leave room for adjustment in special circumstances. The safety time interval is set to 4 minutes and can be adjusted according to the specific situation. The formula is as follows:

[0032] in, Indicates flight k Arrival time; Indicates flight k departure time.

[0033] (4) Large parking stands have the highest utilization rate: Parking stands can be divided into three types according to size: large, medium, and small. Among them, large parking stands have the best facilities and can effectively solve the problem of passenger boarding and disembarking congestion. At the same time, the reasonable arrangement of the use of large parking stands can reduce aircraft taxiway waiting and conflicts. Therefore, maximizing the utilization rate of large parking stands is set as the optimization goal, which is expressed as:

[0034] .

[0035] (5) Highest parking space utilization: Maximizing the overall utilization of boarding gates is conducive to the balanced use of airport resources and accelerating flight turnover. This goal is expressed as: .

[0036] (6) Minimum matching difference between flights and parking slots. This objective is expressed as: .

[0037] S1.2. Objective Optimization Function: The parking space allocation problem has different objectives depending on different needs and situations. This paper selects several main objectives as optimization objects and comprehensively considers them to obtain an optimization model, specifically including:

[0038] The most balanced parking stand idle time: Minimizing parking stand idle time is a key factor in improving parking stand utilization and overall surface resource utilization efficiency. By rationally arranging flight parking stands and ensuring efficient parking stand turnover between different flights, the overall operational efficiency of the airport can be improved. Calculate the idle time between consecutive uses of each parking stand, square it to amplify the effect, and then sum the idle time of all parking stands to obtain the final optimization goal. The formula is as follows:

[0039] .

[0040] Shortest Passenger Walking Distance: Minimizing passenger walking distance is an important factor in improving passenger satisfaction and is also key to improving airport service quality. Therefore, minimizing passenger walking distance is set as an optimization goal. The specific formula is as follows:

[0041] .

[0042] Minimize remote parking stands: Parking stands can be divided into close parking stands and remote parking stands according to their distance from the terminal. With the same total number of stands, the higher the proportion of close parking stands, the stronger the airport's comprehensive support capabilities. Close parking stands help to more efficiently utilize terminal facilities, taxiways and other resources, thereby improving the airport's operational efficiency. At the same time, passengers can board and disembark directly through the jet bridge without having to take a shuttle bus, which improves passenger satisfaction while saving valuable field resources. Therefore, through reasonable planning, the use of close boarding gates as much as possible is optimized to minimize the number of flights at remote boarding gates. The specific description is as follows:

[0043] ; in, Indicates parking space On the flight Free time before arrival; Indicates parking space Free time after daily closing tasks are completed; Indicates the number of parking spaces. n Indicates the total number of flights, Represents the corresponding optimization objective function; Indicates the actual allocated parking space flights the number of passengers; Indicates that the passenger has arrived at the boarding gate Required walking distance, is the decision variable for allocating flights to parking spaces. If flight Assigned to a parking stand ,but , otherwise 0; is the remote stand usage indicator variable. If the flight Assigned to a remote stand ,but , otherwise it is 0. The remote parking stand is the parking stand whose distance to the flight is greater than the set distance threshold.

[0044] S1.3, nonlinear processing: taking into account the multiple factors affecting the efficiency of airport operations, a multi-objective model was constructed. Used to represent a set of multi-objective functions. Converting a complex multi-objective model into a single-objective model is beneficial for solving the problem. Common conversion methods include linear weighting method, hierarchical sequential method, target achievement method, utility function method, etc. The present invention selects the linear weighting method, which is easy to operate and flexible to set. When the weighting factor When >0, the objective function can be expressed as:

[0045] Since these different objective functions have their own dimensions, it is necessary to process the objective functions without quantization. ,and , then the objective function type after no quantitative processing is as shown in the following formula:

[0046] The final objective function of the gate assignment problem can be expressed as follows: .

[0047] S2. Hybrid multi-strategy multi-mechanism sparrow search algorithm (MRCFSSA).

[0048] S2.1. Quasi-reflection-based adaptive variation learning strategy The Sparrow Search Algorithm (SSA) exhibits advantages in balancing exploration and exploitation through its bionic producer-scrounger observer framework, but suffers from three key limitations: (1) premature convergence due to uniform population distribution in multimodal landscapes, (2) inefficient threat avoidance due to the rigid observer perturbation strategy, and (3) initialization sensitivity leading to suboptimal baseline search areas. To address these issues, the present invention first integrates a Crossover Optimization (CSO) mechanism into the observer phase, where horizontal crossover enhances the diversity of escape paths through directional cooperation among sparrows, while vertical crossover accelerates convergence by inheriting historical safe positions. However, this CSO-enhanced SSA still faces unresolved challenges: the biased initialization trap and producer stagnation in flat fitness regions. To comprehensively address these shortcomings, the Markov random function (MRCFSSA) algorithm introduces two synergistic innovations. In the initialization phase, a new mutation quasi-reflective strategy is adopted, while in the joiner search phase, a spiral flight strategy is integrated. These improvements diversify the initial population distribution, effectively reduce the risk of falling into local optimality, and dynamically balance extensive exploration with concentrated exploitation.

[0049] In SSA, the initial population (i.e., the positions of individual sparrows) is generated randomly and uniformly within the solution space. Each sparrow's position corresponds to a potential solution to the optimization problem, whose dimensionality is determined by the problem. While this random generation of initial solutions is simple to implement, it suffers from poor convergence speed and accuracy due to its uneven distribution, lack of diversity, inadequate search space coverage, and limitations in solving high-dimensional problems and complex functions.

[0050] To address this problem, some scholars have proposed the Opposition-based Learning (OBL) strategy. Its core is to generate an opposing solution for each solution, then calculate the fitness of the current solution and its opposing solution, and ultimately select the better solution as the next generation candidate solution. The addition of opposing solutions provides additional search directions and expands the search scope. Therefore, it is widely used in various metaheuristic algorithms and improves the algorithm's ability to escape local optimality. The calculation formula is as follows:

[0051] LB is the lower limit of the solution range, UB is the upper limit value, X ( t ) is the solution of the previous generation. Represents the solution of the current generation of backward learning.

[0052] Quasi Opposition-Based Learning (QOBL) is an improved strategy based on Opposition-Based Learning (OBL) proposed by Rahnamayan. First, based on the position of the current solution in the search space, its traditional inverse solution is calculated. Then, by introducing a dynamic adjustment mechanism, a quasi-inverse solution is generated in the intermediate region between the original solution and its inverse solution. Specifically, the quasi-inverse solution can be constrained to the region near the midpoint of the line connecting the current solution and the inverse solution through a mathematical formula. Unlike the strictly symmetric inverse mapping of OBL, QOBL dynamically balances the contradictory relationship between global exploration and local development while maintaining low computational cost by relaxing the rigid boundaries of the inverse mapping. The calculation formula is as follows:

[0053] ; ; ; in, 、 、 represents the solution of the current generation of quasi-reflective learning, factor, Represents the solution of this generation of mutational quasi-reflective learning.

[0054] By introducing an adaptive mutation rate to dynamically integrate global exploration with OBL and local development with QOBL, this paper proposes an adaptive mutation quasi-reflective learning strategy. The adaptive mutation rate decays with the number of iterations. In the early stage, OBL is used with a higher probability to enhance global exploration, while in the later stage, QOBL is used with a lower probability to enhance local development. The formula is as follows:

[0055] ; ; in α is the attenuation parameter, and Represent the minimum and maximum mutation rates of 5% and 20%, respectively; Indicates the location of the current iteration initialization solution; represents the random variation parameter; T represents the total number of iterations, represents the solution of reverse learning.

[0056] S2.2 Levy Flight Levy flight is a random walk model based on a heavy-tailed probability distribution. The step size of a Levy flight strategy follows a power-law distribution, meaning that longer steps decrease the probability of a solution, but there is a significant probability of long steps. This property makes its search efficiency in unknown environments significantly higher than that of traditional Brownian motion. Due to its efficient exploration capabilities, Levy flight is widely used in optimization algorithms such as Cuckoo Search and Particle Swarm Optimization (PSO). By introducing Levy flight, the algorithm can escape local optima during the global search phase, enhancing its ability to explore the solution space.

[0057] The sparrow search algorithm is optimized by simulating the "discoverer-follower-guardian" collaborative mechanism of the sparrow population, but its basic version has certain limitations in the global search stage. First, the discoverer relies on local search with a fixed step size, which can easily fall into local optimality in complex multi-peak problems. Secondly, in the later stages of iteration, the group converges more and more, and the ability to explore unknown areas decreases. To solve the above problems, the present invention applies Levy flight to the discoverer stage, so that individual sparrows will perform long-distance jumps (Levy step length) combined with short-distance fine searches with a certain probability during the search process. Long-step jumps allow some sparrows to escape from the current dense area, reducing resource competition; short-step search ensures local development, and long-step jumps expand the global field of view. The formula is as follows:

[0058] ; ; in Indicates the i Only the sparrow is iterating t Position at +1. The step size factor is used to control the amplitude of the Levy step size to avoid oscillation caused by excessive jumps. Represents the random step size generated by Levy distribution, satisfying , s represents the step size reference value, where The value range of these two parameters is meaningless. is a uniformly distributed random number used to trigger the Levyflight strategy ( ), is the trigger threshold, is a stabilizing parameter used to control the shape of the step size distribution; 𝜆 controls the jump amplitude of the Levy distribution; 𝑄⋅𝐿 represents the random disturbance term composed of the disturbance factor 𝑄 and the step size 𝐿.

[0059] S2.3, cross optimization strategy.

[0060] Crisscross Optimization (CSO) is an intelligent optimization algorithm based on cross-search in multidimensional space. It aims to address the premature convergence problem of traditional optimization algorithms in multimodal, high-dimensional problems by collaboratively searching horizontally (between individuals of the same generation) and vertically (between individuals of different generations). As the name suggests, the Crisscross Optimization (CSO) algorithm's mechanism can be divided into two directions: horizontal cross-search and vertical cross-search.

[0061] Horizontal crossover simulates the situation when a flock of sparrows encounters a threat. Individuals exchange information through chirping and flight paths, quickly sharing escape directions and forming a distributed escape network. This allows individuals of the same generation to exchange information across different dimensions of the solution space, thereby enhancing local development capabilities. The vertical crossover strategy draws on the population's intergenerational memory, allowing young individuals to incorporate past successful escape experiences and reduce repeated exploration of ineffective areas. Individuals of the current generation are mixed with historically successful individuals along specific dimensions, simulating "intergenerational experience inheritance" and maintaining population diversity.

[0062] In the basic SSA algorithm, the sentinel is responsible for escaping from the dangerous area, but its original update strategy relies on random perturbations, which leads to the defects of limited exploration direction and inability to fully utilize historical safety information. Therefore, the present invention integrates the vertical and horizontal cross algorithm position update strategy into the sentinel position update phase of SSA. The integration of the CSO strategy enables the sentinel to consider both real-time collaboration and historical experience, thereby improving the search efficiency. , select paired individuals according to their position parity, when j When it is an odd number, the next individual j +1 crossover, when j When it is an even number, it is the same as the previous individual j -1 crossover, the specific formula is designed as follows:

[0063] in Indicates the j Individuals in i The location of the dimension, r Represents a uniformly distributed random number ( ), which is used to control the ratio of information fusion between individuals. c is the disturbance factor, which is used to introduce random disturbances and enhance the exploration ability ( ).

[0064] At the same time, for each individual vigilant , randomly select two of its dimensions and , to fuse information between dimensions: Indicates the updated j The first vigilante i Dimensional location information, Indicates the j The location information of each sentinel.

[0065] in is a uniformly distributed random number , control the information exchange ratio of different dimensions, represents two different dimensions randomly selected from the dimension set ( ).

[0066] Experiments have shown that: Data Source and Parameter Settings: To validate the MRCFSSA's performance in real-world parking stand allocation, we selected data from Guangzhou Baiyun Airport in China. This data includes 30 large, medium, and small parking stands and 250 flights. Based on these constraints, we conducted a flight pre-assignment experiment to the gates. Table 2 shows gate-related information, and Table 3 shows selected flight information.

[0067] For parameter settings, the proportion of producers is set to 20%, the proportion of guards is set to 20%, the number of individuals in the population is set to 30 based on the actual situation of the gate allocation problem, and the number of iterations is set to 200. Finally, the three weights of the objective function formula are set to =0.25, =0.25, =0.2, =0.1, =0.1, = 0.1. Each experiment was run 50 times independently to ensure the reliability of the experimental results.

[0068] Table 2. Gate related information Table 3 Partial flight information Experimental results and analysis Verify the optimization performance of MRCFSSA in the gate allocation problem. On this basis, different improved sparrow search algorithms are used to solve the multi-objective optimization model of the parking space allocation problem. Each algorithm and strategy is run independently 50 times with the same parameters. The MRCFSSA algorithm is compared with DBO, GWO, SSA, WOA, HHO, AVOA, SCSO, GEO, FHO, RSO, SMA and ISSA1, ISSA2, ASFSSA, EMSSA algorithms. The accuracy of the target value and the maximum allocation rate are the main indicators for evaluating the results of the gate allocation problem. Among the 50 times, the one with the best target value is selected for experimental analysis. The pre-allocation results are shown in Figure 2. The Gantt chart is shown in Figure 2. Figure 3 The experimental results of various indicators and the comparison of convergence curves with MRCFSSA and 11 basic algorithms and 4 improved sparrow search algorithms are shown in Table 5 and Figure 4 As shown in the figure, the convergence curves show that MRCFSSA outperforms other algorithms in terms of convergence speed, convergence accuracy, and solution stability. Experimental comparisons with MRCFSSA and various state-of-the-art algorithms show that MRCFSSA achieves the best result, reaching 0.6469. MRCFSSA also achieves the best stability, reaching 5.327E-03. The flight matching rate reaches 98.00%. Comparisons show that MRCFSSA outperforms other algorithms. However, in terms of its own improvements, the time complexity increases with the addition of strategies, with MRCFSSA requiring the longest time. The combination and incorporation of various improved strategies leads to improved performance compared to the basic sparrow search algorithm. Experimental results show that the average runtime of MRCFSSA is longer than that of 11 basic intelligent optimization algorithms and shorter among the improved sparrow search algorithms.

[0069] Table 4 Results of 11 basic algorithms and 4 improved sparrow search algorithms In summary, the MRCFSSA algorithm can reduce route costs, improve comprehensive service quality, and provide an effective and robust reference for gate allocation. The algorithm is an efficient and robust multi-strategy and multi-mechanism hybrid sparrow search algorithm.

[0070] The MRCFSSA proposed in the present invention is based on adaptive variation quasi-reflective learning, vertical and horizontal cross strategy and Levy flight strategy. The space of initialization solutions of the basic algorithm is expanded by the improved reflective learning strategy, and the quality of the initial solution is improved. The vertical and horizontal cross strategy enhances the ability of the algorithm to jump out of the local optimum, and the Levy flight strategy enhances the convergence of the algorithm. The combination of the three strategies balances the relationship between global search and local search as a whole, and improves the comprehensive search capability of the algorithm. The present invention uses 47 basic test functions and 20 basic functions from cec2017, cec2014, and cec2005 to verify the performance of MRCFSSA. The experimental results show that whether compared with the latest basic group intelligent optimization algorithm or SSA related variants, MRCFSSA can show faster convergence speed and higher convergence accuracy. At the same time, through comparative experiments, it is verified that MRCFSSA still has high convergence accuracy in different dimensions and the optimization effect is stable. MRCFSSA is applied to the actual engineering problem of parking space allocation to verify its ability to handle complex multi-constraint problems. A parking stand allocation optimization model was constructed with the goals of balancing stand idle time, minimizing passenger walking distance, minimizing the number of remote stands, maximizing large stand utilization, maximizing overall stand utilization, and maximizing stand-to-flight matching. Experimental results showed that the MRCFSSA algorithm achieved an average convergence accuracy of 0.6496, a 15% improvement over the basic SSA algorithm. This algorithm is capable of generating effective and balanced parking stand allocation solutions.

[0071] The proposed MRCFSSA, based on a combination of three strategies—adaptive variational quasi-reflective learning, a cross-cutting strategy, and a Levy flight strategy—balances global and local search, improving the algorithm's comprehensive search capabilities. For the parking stand allocation problem, the proposed multi-objective model comprehensively considers six key metrics: parking stand availability balance, passenger walking distance, and minimization of remote stand allocation. Integrating complex constraints through a linear weighting method, experiments have verified that its actual allocation rate reaches 98%, significantly improving resource utilization efficiency and enhancing the passenger experience (shortened walking distance) compared to traditional algorithms. Furthermore, a case study at Guangzhou Baiyun Airport demonstrated that the MRCFSSA exhibited strong robustness, achieving a standard deviation of only 5.327E-03 in 50 independent runs, while maintaining comparable runtime to mainstream algorithms. This demonstrates its high precision, strong stability, and engineering practicality, providing an efficient solution for complex dynamic airport scheduling.

[0072] Based on the same inventive concept, the present invention also proposes an airport parking stand allocation system, comprising: The model building module is used to obtain multiple parking stands and flights of different airport models; the corresponding relationship between parking stands and flights is used as the decision variable, the most balanced parking stand idle time, the minimized passenger walking distance and the minimum number of remote parking stands are used as the objective function, and the maximum utilization rate of the largest parking stand model, the maximum overall parking stand utilization rate, and the maximum parking stand and flight matching rate are used as constraints to construct a parking stand allocation optimization model.

[0073] The solution module is used to treat the allocation plans of all flights and parking spaces as a population and each flight and parking space allocation plan as an individual, and use the improved sparrow search algorithm to solve the parking space allocation optimization model with the minimization objective function as the fitness function. The solution process specifically includes: generating an initial population, calculating the adaptive variation quasi-reflective solution of each individual in the initial population, calculating the fitness value of each individual and the adaptive variation quasi-reflective solution, selecting the individual with the better current fitness value to update the initial population, and obtaining an updated population; calculating the fitness value of each individual in the updated population and sorting them to determine the discoverer individual, follower individual, and guard individual; generating a random number for each discoverer individual, and if the random number is less than a set threshold, triggering the Levy flight strategy and generating the Levy step size; updating the position of the discoverer individual according to the Levy step size; the follower individual moves closer to the discoverer individual according to the random perturbation, and at the same time introducing a vertical and horizontal cross strategy to update the position of each guard individual to generate the optimal allocation plan between flights and parking spaces.

[0074] The allocation module is used to allocate airport parking spaces according to the optimal allocation plan between flights and parking spaces.

[0075] The present invention also provides an airport parking stand allocation computer device, comprising: a memory, a processor, and a computer program stored in the memory, wherein the processor implements the steps of the airport parking stand allocation method when executing the computer program.

[0076] The present invention also provides a readable storage medium, which stores a computer program. The computer program includes program instructions. When the program instructions are executed by a processor, they are used to execute the steps of the airport parking space allocation method.

[0077] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A method for allocating parking spaces at an airport, characterized in that: The following steps are involved: Obtain multiple parking stands and flights of different airport models; use the correspondence between parking stands and flights as the decision variable, and the objective function of maximizing the idle time of parking stands, minimizing the passenger walking distance, and minimizing the number of remote parking stands. Construct a parking stand allocation optimization model with the maximum utilization rate of the largest parking stand, the maximum overall parking stand utilization rate, and the maximum parking stand and flight matching rate as constraints. The allocation schemes of all flights and parking spaces are regarded as a population, and each flight and parking space allocation scheme is regarded as an individual. The minimization of the objective function is used as the fitness function, and the improved sparrow search algorithm is used to solve the parking space allocation optimization model. The solution process specifically includes: generating an initial population, calculating the adaptive variation quasi-reflective solution for each individual in the initial population, calculating the fitness value of each individual and the adaptive variation quasi-reflective solution, selecting the individual with the better current fitness value to update the initial population, and obtaining the updated population; calculating the fitness value of each individual in the updated population and sorting them, and determining the discoverer individual, follower individual, and guard individual; generating a random number for each discoverer individual, and if the random number is less than the set threshold, triggering the Levy flight strategy and generating the Levy step size; updating the discoverer individual position according to the Levy step size; the follower individual moves closer to the discoverer individual according to the random perturbation, and at the same time introducing the vertical and horizontal cross strategy to update the position of each guard individual, and generating the optimal allocation plan between flights and parking spaces; Allocate airport parking spaces based on the optimal allocation plan between flights and parking spaces.

2. The method for allocating an airport parking space according to claim 1, wherein: The objective function is to optimize the idle time of the most balanced parking stands, minimize the passenger walking distance, and minimize the number of remote stands. Specifically, the optimization objective of optimizing the idle time of the most balanced parking stands is obtained by calculating the idle time of each parking stand between consecutive uses and summing the idle time of all parking stands. The optimization objective is expressed as: According to the shortest walking distance between passengers and parking stands, the optimization goal of minimizing the walking distance of passengers is obtained, which is expressed as: According to the distance between the parking stand and the terminal, the optimization goal is to minimize the number of flights at the gate farthest from the parking stand, which can be expressed as: ； in, Indicates parking space On the flight Free time before arrival; Indicates parking space Free time after daily closing tasks are completed; Indicates the number of parking spaces. n Indicates the total number of flights, Represents the corresponding optimization objective function; Indicates the actual allocated parking space flights the number of passengers; Indicates that the passenger has arrived at the boarding gate Required walking distance, is the decision variable for allocating flights to parking spaces. If flight Assigned to a parking stand ,but , otherwise 0; is the remote stand usage indicator variable. If the flight Assigned to a remote stand ,but , otherwise it is 0. The remote parking stand is the parking stand whose distance to the flight is greater than the set distance threshold.

3. The method for allocating an airport parking space according to claim 2, wherein: The constraints of the maximum utilization rate of large parking stands, the overall utilization rate of the maximum parking stands, and the maximum parking stand and flight matching rate specifically include: A flight can only occupy one parking space within the specified time, which is expressed as: ； The parking stand size and flight size are divided into three categories according to actual conditions. The size of the flight parked on the parking stand must not exceed the parking stand size, which is expressed as: ； The pushback time between two consecutive flights at the same parking stand must be at least the set safety time, which is expressed as: ； The parking spaces are divided into three types: large, medium, and small according to the threshold value. The optimization goal is to maximize the utilization rate of large spaces, which can be expressed as: ； Maximize the overall utilization of the boarding gate and speed up the flight turnaround, expressed as: ； Minimize the matching difference between flights and slots, expressed as: ； in, Represents a 0-1 variable indicating the flight Assigned to the apron; Indicates the model of the parking stand; Indicates the flight type; Indicates flight k Arrival time; Indicates flight k departure time; Indicates flight i Parking at a gate that is not the correct size for the aircraft j Department; Indicates flight i Assigned to a large parking stand j .

4. The method for allocating an airport parking space according to claim 1, wherein: The method of calculating the reverse solution and the quasi-reverse solution for each individual in the population and calculating the adaptive mutation rate according to the current number of iterations specifically includes the following steps: Constraining the quasi-reverse solution to the area near the midpoint of the line connecting the current solution and the reverse solution yields: ； ； in, 、 Indicates the middle value of the range. represents the solution of the current generation of quasi-reflective learning, is a random factor between 0 and 1, represents the solution of this generation of mutational quasi-reflective learning; By introducing adaptive mutation rate to dynamically integrate the global exploration of OBL and the local development of QOBL, we can obtain: ； ； in α is the attenuation parameter, and represent the minimum mutation rate and the maximum mutation rate, respectively. Indicates the location of the current iteration initialization solution; represents the random variation parameter; T represents the total number of iterations, represents the solution of reverse learning.

5. The method for allocating an airport parking space according to claim 1, wherein: A random number is generated for each individual discoverer. If the random number is less than a set threshold, Levy flight is triggered, a Levy step length is generated, and the individual discoverer position is updated according to the Levy step length. The process is expressed as follows: ； ； in Indicates the i Only the sparrow is iterating t +1 position, is the step size factor used to control the magnitude of the Levy step size, Represents the random step size generated by Levy distribution, satisfying , s represents the step size reference value, where , It is a uniformly distributed random number used to trigger the Levy flight strategy. is the trigger threshold, is a stabilizing parameter used to control the shape of the step size distribution; 𝜆 controls the jump amplitude of the Levy distribution; 𝑄⋅𝐿 represents the random disturbance term composed of the disturbance factor 𝑄 and the step size 𝐿.

6. The method for allocating an airport parking space according to claim 1, wherein: The introduction of the vertical and horizontal cross strategy to update the position of each individual sentry specifically includes the following steps: For the Vigilant , select paired individuals according to their position parity, when j When it is an odd number, the next individual j +1 crossover, when j When it is an even number, it is the same as the previous individual j -1 crossover, which are represented by: in Indicates the j Individuals in i Dimensional location; r represents a uniformly distributed random number, ; c is the disturbance factor, ; For each individual vigilant , randomly select two of its dimensions and , to fuse information between dimensions: in is a uniformly distributed random number, ; represents two different dimensions randomly selected from the dimension set, 、 、 Respectively represent the updated j The first vigilante i Dimensional location information.

7. An airport parking stand allocation system, characterized in that: include: Model building module for acquiring multiple parking spaces and flights of different airport models; The correspondence between parking stands and flights is used as the decision variable, and the objective function is to achieve the most balanced parking stand idle time, minimize passenger walking distance, and minimize the number of remote stands. A parking stand allocation optimization model is constructed with the maximum utilization rate of the largest parking stand, the maximum overall parking stand utilization rate, and the maximum parking stand and flight matching rate as constraints. The solution module is used to treat the allocation plans of all flights and parking spaces as a population, and the allocation plan of each flight and parking space as an individual, with the minimization of the objective function as the fitness function, and adopt the improved sparrow search algorithm to solve the parking space allocation optimization model; the solution process specifically includes: generating an initial population, calculating the adaptive variation quasi-reflective solution of each individual in the initial population, and selecting the individual with the better current fitness value to update the initial population by calculating the fitness value of each individual and the adaptive variation quasi-reflective solution to obtain an updated population; calculating the fitness value of each individual in the updated population and sorting them to determine the discoverer individual, follower individual and guard individual; generating a random number for each discoverer individual, and if the random number is less than the set threshold, triggering the Levy flight strategy and generating the Levy step length; updating the discoverer individual position according to the Levy step length; the follower individual moves closer to the discoverer individual according to the random perturbation, and at the same time introducing the vertical and horizontal cross strategy to update the position of each guard individual to generate the optimal allocation plan between flights and parking spaces; The allocation module is used to allocate airport parking spaces according to the optimal allocation plan between flights and parking spaces.

8. An airport parking stand allocation computer device, characterized in that: include: A memory, a processor, and a computer program stored in the memory, wherein when the processor executes the computer program, the steps of the airport parking stand allocation method according to any one of claims 1 to 6 are implemented.

9. A readable storage medium, characterized in that: The readable storage medium stores a computer program, which includes program instructions. When the program instructions are executed by a processor, they are used to execute the steps of the airport parking stand allocation method according to any one of claims 1 to 6.

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